Graph y^2+3x=0

Problem

y2+3*x=0

Solution

1. Identify the type of equation. Since the equation has one variable squared (y2 and one variable to the first power (x, it represents a parabola.

2. Isolate the x variable to determine the orientation. Subtract y2 from both sides and divide by 3

3*x=−y2

x=−1/3*y2

3. Determine the vertex and axis of symmetry. The equation is in the form x=a*(y−k)2+h where (h,k) is the vertex. Here, h=0 and k=0 so the vertex is at (0,0) The axis of symmetry is the x-axis (y=0.

4. Analyze the direction of opening. Since the coefficient a=−1/3 is negative and the equation is solved for x the parabola opens to the left.

5. Find additional points to plot. Choose values for y and solve for x
   If y=3 then x=−1/3*(3)2=−3 Point: (−3,3)
   If y=−3 then x=−1/3*(−3)2=−3 Point: (−3,−3)

6. Sketch the graph by plotting the vertex (0,0) and the points (−3,3) and (−3,−3) then drawing a smooth curve opening to the left.

Final Answer

x=−1/3*y2

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